Planar silicon ring structures are commonly used in Micro-Electro-Mechanical-Systems (MEMS) gyroscopes. Examples of such devices are described in U.S. Pat. No. 5,932,804 and U.S. Pat. No. 6,282,958. Gyroscope devices utilising these resonator designs are used in a range of automotive and commercial applications. The performance of these devices may also be suitable for use in some guidance and control applications for example, for guided projectiles where the flight time is relatively short (tens to hundreds of seconds). For applications where longer operating times are required, the performance of these devices may not be sufficiently accurate with the magnitude of the bias drift error being particularly problematic.
One of the primary factors limiting the bias drift performance is the Quality Factor (Q) of the resonator structure. A high Q is beneficial in reducing the drive voltage that must be applied to set the primary mode into resonance. Cross-coupling of this drive signal into the rate sensing channel is one of the main error drivers for the bias stability where the coupled signal is indistinguishable from that produced by an applied rotation rate. Other bias errors associated with transducer misalignment and damping non-uniformity may also be significantly reduced by increasing the Q value of the resonator.
In MEMS devices the Q is determined by a number of contributory damping factors. The effective Quality Factor, QEff, will be determined by the sum of all of these damping contributions and may be expressed as:
                              1                      Q            Eff                          =                              1                          Q              TE                                +                      1                          Q              Gas                                +                      1                          Q              Other                                                          (        1        )            where QTE is the thermoelastic damping contribution, QGas the gas damping contribution and Qother includes contributions from support losses, intrinsic material losses and electronics damping.
Gyroscopic devices based on the resonator design of U.S. Pat. No. 5,932,804 use a ring structure which has an outer diameter of 6 mm and a rim thickness of 120 microns. This structure is operated in a partial vacuum with a 10 Torr residual pressure of dry Nitrogen (room temperature value). The QEff value for this device has been shown to be 5000 and has been shown to result from approximately equal contributions from the thermoelastic and gas damping with the Qother contribution being significantly lower. Therefore, even under high vacuum the QEff value will be limited to 10,000 by the thermoelastic damping.
The mechanism of thermoelastic damping in MEMS resonators is well known to those skilled in the art and will only be described in summary here to aid the understanding of the invention. As the resonator oscillates in the cos 2θ flexural mode, the ring will be subject to cyclic compressive and tensile stresses around the vibration anti-nodes at the inner and outer vertical surfaces. Where the ring is compressed there will be a slight increase in temperature and, where the ring is in tension, there will be a slight reduction in temperature, setting up a temperature gradient across the ring. This temperature gradient will alternate as the ring oscillates. There will thus be a time dependent heat flow across the ring. Relaxation occurs as the heat flows from the hotter compressed region to the cooler extended region of the ring with an associated time constant, τ. The relaxation time depends on the length of the temperature gradient (in this case the ring width, rt) and the thermal diffusivity of the material, χ, as described in the following equation:
                              τ          r                =                              r            t            2                                              π              2                        ⁢            χ                                              (        2        )            
The intrinsic damping is a function of the relaxation time, the frequency at which the structure vibrates and a number of material properties. The loss factor is given by:
                              η          r                =                                            E              ⁢                                                          ⁢                              α                2                            ⁢              T                                      C              V                                ⁢                                                    ω                n                            ⁢                              τ                r                                                    1              +                                                ω                  n                  2                                ⁢                                  τ                  r                  2                                                                                        (        3        )            where E, α, and CV are the Young's modulus, thermal expansion coefficient and heat capacity per unit volume of the material, in this case silicon, ωη is the oscillation frequency and T is the ambient temperature respectively. The QTE factor is given by:
                              Q          TE                =                  1                      η            r                                              (        4        )            
Examination of equations 3 and 4 shows that the QTE factor will be a minimum when the operating frequency coincides with the peak loss frequency, ωmax which is given by:
                              ω          max                =                              1                          τ              r                                =                                                    π                2                            ⁢              χ                                      r              t              2                                                          (        5        )            
The variation of the loss factor with frequency for a 6 mm silicon ring structure, as used in products based on the design of U.S. Pat. No. 5,932,804, is shown in FIG. 1. It can be seen that the peak loss occurs at around 10 kHz. The cos 2θ operating frequency for this device is at 14 kHz and is therefore nearly coincident with the peak loss frequency. This means that the thermoelastic damping is approaching a maximum value and the calculated QTE value is very close to the experimental observed value of ˜10,000.
Some improvement in the QEff for this device can be achieved by packaging the resonator at a reduced pressure however the increase is fundamentally limited by the thermoelastic damping. Significantly enhancing the QEff for this device can only be achieved if the QTE contribution can be reduced. Conventionally, reduction of this term requires the rim thickness, rt, to be changed, thus changing the loss frequency. This will however result in a shift in the resonant frequency which would necessitate undesirable changes to the control electronics. The QTE can be effectively increased without shifting the cos 2θ resonance frequency by reducing the ring diameter and the rim thickness in appropriate proportions. However, while this does enable QTE, to be increased, the smaller geometry will have a detrimental effect on other aspects of the device performance. In particular, the signal to noise ratio will be reduced due to the reduction in the size of the sensing transducers. Also, the mechanical tolerances of the fabrication process will become more critical which can adversely affect the production yield. Further changes would be required to the magnetic circuit components which would also result in adverse changes to both scalefactor and bias performance characteristics.
The above discussion relates particularly to the 6 mm ring implementation of the design described in U.S. Pat. No. 5,932,804. However, it will be appreciated that similar considerations apply to devices which are being produced based on the design described in U.S. Pat. No. 6,282,958. Practical devices utilising 4 mm and 8 mm diameter rings have been produced. The QEff for these designs has been shown to be similarly limited by the thermoelastic damping to varying degrees.
It would therefore be beneficial to be able to have the capability to adjust the peak loss frequency independently of the ring diameter and rim thickness in order to increase the QTE for typical ring structures. This would enable improvements to be made to the critical bias drift error without adversely affecting other performance parameters or the production yield and without necessitating any changes in the control electronics.